{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian Data Analysis, 3rd ed\n",
    "## Chapter 2, demo 2\n",
    "\n",
    "Authors:\n",
    "- Aki Vehtari <aki.vehtari@aalto.fi>\n",
    "- Tuomas Sivula <tuomas.sivula@aalto.fi>\n",
    "\n",
    "Probability of a girl birth given placenta previa (BDA3 p. 37).\n",
    "Illustrate the effect of a prior. Comparison of posterior distributions with different parameter values for Beta prior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# import necessary packages\n",
    "\n",
    "import numpy as np\n",
    "from scipy.stats import beta\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# add utilities directory to path\n",
    "import os, sys\n",
    "util_path = os.path.abspath(os.path.join(os.path.pardir, 'utilities_and_data'))\n",
    "if util_path not in sys.path and os.path.exists(util_path):\n",
    "    sys.path.insert(0, util_path)\n",
    "\n",
    "# import from utilities\n",
    "import plot_tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# edit default plot settings\n",
    "plt.rc('font', size=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# grid\n",
    "x = np.linspace(0.375, 0.525, 150)\n",
    "\n",
    "# posterior with data (437,543) and uniform prior Beta(1,1)\n",
    "au = 438\n",
    "bu = 544\n",
    "# calculate densities\n",
    "pdu = beta.pdf(x, au, bu)\n",
    "\n",
    "# compare 3 cases\n",
    "# arrays of different priors:\n",
    "# Beta(0.485*n, (1-0.485)*n), for n = 2, 20, 200\n",
    "ap = np.array([0.485 * (2*10**i) for i in range(3)])\n",
    "bp = np.array([(1-0.485) * (2*10**i) for i in range(3)])\n",
    "# corresponding posteriors with data (437,543)\n",
    "ai = 437 + ap\n",
    "bi = 543 + bp\n",
    "# calculate prior and posterior densities\n",
    "pdp = beta.pdf(x, ap[:,np.newaxis], bp[:,np.newaxis])\n",
    "pdi = beta.pdf(x, ai[:,np.newaxis], bi[:,np.newaxis])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above two expressions uses numpy broadcasting inside the `beta.pdf` function. Arrays `ap` and `bp` have shape (3,) i.e. they are 1d arrays of length 3. Array `x` has shape (150,) and the output `pdp` is an array of shape (3, 150).\n",
    "\n",
    "Instead of using the `beta.pdf` function, we could have also calculated other arithmetics. For example\n",
    "```python\n",
    "out = x + (ap * bp)[:, np.newaxis]\n",
    "```\n",
    "returns an array of shape (3, 150), where each element ``out[i, j] = x[j] + ap[i] * bp[i]``.\n",
    "\n",
    "With broadcasting, unnecessary repetition is avoided, i.e. it is not necessary to create an array of `ap` repeated 150 times into the memory. More info can be found on the numpy documentation (search for broadcasting)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
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h93vU1DVy2y//zfAhMTxx19VgAmDcXOdSnsincQXA2LkEBAXz4gNfxO22/OzF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h9//LF8vOSsrCzk5OTI56PNy8vDzp075Y8FugoKpkT1KosUTwStawzYDe749JCn+vLLLzF8+L/P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\nA3YYmtf7zNXJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbc06e898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot 3 subplots\n",
    "fig, axes = plt.subplots(\n",
    "    nrows=3, ncols=1, sharex=True, sharey=True, figsize=(8, 12))\n",
    "# show only x-axis\n",
    "plot_tools.modify_axes.only_x(axes)\n",
    "# manually adjust spacing\n",
    "fig.subplots_adjust(hspace=0.4)\n",
    "\n",
    "# 3 subplots\n",
    "for i, ax in enumerate(axes):\n",
    "    # plot three precalculated densities\n",
    "    post1, = ax.plot(x, pdu, color=plot_tools.lighten('C1'), linewidth=5)\n",
    "    prior, = ax.plot(x, pdp[i], 'k:')\n",
    "    post2, = ax.plot(x, pdi[i], color='k', dashes=(6, 8))\n",
    "    # add vertical line\n",
    "    known = ax.axvline(0.485, color='C0')\n",
    "    # set the title for this subplot\n",
    "    ax.set_title(\n",
    "        r'$\\alpha/(\\alpha+\\beta) = 0.485,\\quad \\alpha+\\beta = {}$'\n",
    "        .format(2*10**i)\n",
    "    )\n",
    "# limit x-axis\n",
    "axes[0].autoscale(axis='x', tight=True)\n",
    "axes[0].set_ylim((0,30))\n",
    "# add legend to the last subplot\n",
    "axes[-1].legend(\n",
    "    (post1, prior, post2, known),\n",
    "    ( 'posterior with uniform prior',\n",
    "      'informative prior',\n",
    "      'posterior with informative prior',\n",
    "     r'known $\\theta=0.485$ in general population'),\n",
    "    loc='upper center',\n",
    "    bbox_to_anchor=(0.5, -0.2)\n",
    ");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
